Producing interpretable local models in parametric CMAC by regularization

Abstract

Cerebellar model articulation controller (CMAC) has been widely applied to modeling and control due to its attractive features such as fast training speed and parsimonious structure. A parametric CMAC is a CMAC model with its constant weights replaced by linear functional weights or linear local models, i.e., a type of Tagaki-Sugeno fuzzy model. This paper proposes a regularized parametric CMAC, and investigates how its linear local models are able to approximate the local linearity of the nonlinear system to be modeled by using regularization techniques and how the regularized parametric CMAC can be successfully applied in modeling a nonlinear process for state estimation of unknown nonlinear processes. Experimental results on the approximation ability and interpretability of the regularized parametric CMAC and its application to nonlinear state estimation have been presented to demonstrate the advantages of the regularized parametric CMAC.